Ppk Calculator
Long-term process performance against the nearer specification limit.
What this calculator does
Both one-sided indices are computed and the smaller is reported; Pp and the distance of the mean from centre are shown alongside.
Inputs and what they mean
- Upper specification limit
- — number value.
- Lower specification limit
- — number value.
- Process mean
- — number value.
- Overall standard deviation
- — Overall (long-term) standard deviation of all the individual measurements, including the drift between subgroups..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Ppk = min[(USL − μ) ÷ (3σ_overall), (μ − LSL) ÷ (3σ_overall)]
Worked example
Mean 10.02 in a 9.5 to 10.5 specification, overall sigma 0.15
The nearer specification limit sets the index.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
Results depend entirely on the figures you enter and are rounded for display. They are for general information and education, not professional advice.
Reference: National Institute of Standards and Technology — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Formula, source and verification
The smaller of the two one-sided performance indices, using the overall standard deviation.
The question it answers: How does the process perform over the long run, and what sigma level does its defect rate imply?
The formula
Ppk = min[(USL − μ) ÷ (3σ_overall), (μ − LSL) ÷ (3σ_overall)]
- USL — Upper specification limit
- (measurement). Highest acceptable value.
- LSL — Lower specification limit
- (measurement). Lowest acceptable value.
- μ — Process mean
- (measurement). Average of the individual measurements.
- σ_overall — Overall standard deviation
- (measurement). Long-term variation of all individual measurements.
Units: Specification, mean and standard deviation in the same measurement unit; the index is dimensionless.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
Both one-sided indices are computed and the smaller is reported; Pp and the distance of the mean from centre are shown alongside.
Assumptions built into the result
- Statistical: The standard deviation supplied is an overall (long-term) estimate.
Figures this calculator will never guess for you
- No benchmark, target or 'world class' value is supplied or implied; the result describes only the figures entered.
- Ppk is never presented as interchangeable with Cpk; the two use different standard deviations.
- No minimum acceptable Ppk is stated.
Limitations
- Interpretation assumes measurements that are approximately normal over the period.
- The index describes the period measured; it does not predict a different period.
- A performance index, an industry benchmark and a customer's required index are three different things.
Source and version
- Standard or reference
- Process performance index Ppk — NIST/SEMATECH (NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices: the one-sided indices are taken against each limit and the smaller is reported.)
- Published source
- National Institute of Standards and Technology — e-Handbook
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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